Hello wGatsby,
This doesn't really happen to often. Most of the time when you need to go down into the core you either have the miner, a kit with a pickaxe, or a way to get back out. Also if you really are stuck you could have always mined out of it with your hand. It would take a bit but at least you would get out.
In a way I kind of like this idea. I for one play defensive a lot and not being able to get out bothers me sometimes. Although if I get stuck in the core usually someone comes in and kills me or I mine out.
Because this is not too much of a problem and there are ways to get around it already, I do not think this will be added. Maybe in the future if something changes where there is not a way you can get around this problem it may be added. Otherwise cool suggestion!